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I'm calling apply(data, 2, function(x) {...}) where data is a matrix. Is there any way for the function to know the name of the column whose values are present in x? Or perhaps there's another function to accomplish the same task?

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One common way to deal with this is to loop over the column names themselves:

m <- matrix(runif(16),4,4)
colnames(m) <- letters[1:4]
sapply(colnames(m),function(x){mean(m[,x])})
        a         b         c         d 
0.4720319 0.4992337 0.5026318 0.3514267

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